With rapid advance in technology along with the development in industrial production, the demands for better precision on surface profilometry with respect to geometrical sizes, surface roughness and free-form surfaces is even increasing. However, since the measurements of all those surface profilometry techniques currently available are easily affected by environment disturbances and thus causing undesired errors in the measurements, it is in urgent needs of improved real-time three-dimensional surface profilometry techniques.
There are already many studies relating to such improved real-time three-dimensional surface profilometry techniques. One of which is a three-dimensional surface profilometry technique disclosed in U.S. Pat. No. 4,768,881, entitled “Method and apparatus for processing holographic interference patterns using Fourier-transforms”. Operationally, after projecting a fringe pattern onto an object to be measured, the object is first being imaged by a square-shaped imaging unit for obtaining an spatial image including only the portion of the object in the square area defined by the imaging unit, and then the so-obtained spatial image of the object is transformed into a frequency-domain image which is then being filtered by a band-pass filter for obtaining phase information relating to the frequency-domain image to be further used for reconstructing the three-dimensional surface profile of the object.
Moreover, there is another prior-art surface profilometry method disclosed by Cedric Breluzeau, et al. in “Automated fringe-pattern extrapolation for patterned surface profiling by interference microscopy with Fourier transform analysis’, Proceedings of SPIE, vol. 5858, 2005, which uses an adjustable band-pass filter to set a threshold value for the purpose of achieving optimal filtering while preventing causing any measurement error in the intended three-dimensional surface reconstruction. Although different filter shapes in the Fourier space were tested for the determination of valid areas in the interferogram, only the neighboring areas with the most significant spectral signals are selected to be the valid areas by those filters of different shapes. Thus, it does not extract the entire vital spectrum precisely required for accurate phase information reconstruction. Therefore, there may be distortion in the reconstructed surface profile basing upon the aforesaid methods, which is especially true for reconstructing those objects with sharp edges.
It is noted that all the aforesaid surface profilometry measurement techniques use a band-pass filter as a means for defining a valid area in a frequency spectrum of a deformed structured fringe pattern and thus obtaining phase information from the valid area to be used in a calculation for reconstructing surface profile of the object. However, as the valid area defined by the conventional band-pass filters, such as 2-D Hanning filter or circular band-pass filters, used in the aforesaid surface profilometry measurement techniques fails to include all the spectrum areas containing vital phase information of the object's surface profile, the reconstructed surface profile of the object resulting from the foregoing reconstruction calculations may deviate from the actual surface profile of the object in size or in shape which severely affects the accuracy of the surface profilometry. Please refer to FIG. 1A to FIG. 1G, which show various reconstructed images of a ball-shaped object relating to different stages in a surface reconstruction process using a conventional circular band-pass filter. FIG. 1A is a spatial domain image (deformed structured fringe pattern) of a ball-shaped object using fringe projection. FIG. 1B is a frequency domain image obtained by performing a Fourier transformation upon the image of FIG. 1A. FIG. 1C shows a spectrum information which is obtained by circular band-pass filtering the area in the image of FIG. 1B within the +1 order and −1 order frequency spectrum areas. FIG. 1D is an image obtained by performing an inverse Fourier transformation upon the spectrum information of FIG. 1C. For reconnecting the phase discontinuities in the image of FIG. 1D, a Euler transformation and a phase unwrapping process is performed upon the image of FIG. 1D for achieving a continuous phase distribution, as shown in FIG. 1E. Using the information of continuous phase distribution in FIG. 1E, the surface profile of the ball-shaped object can be reconstructed, as the reconstructed three-dimensional image shown in FIG. 1F and a cross-sectional image of the profile illustrated in FIG. 1G.
Please refer to FIG. 1H to FIG. 1L, which show various reconstructed images of a ball-shaped object relating to different stages in a phase unwrapping process using another conventional circular band-pass filter disclosed by Cédric Bréluzeau, et al. FIG. 1H shows an overlapping step-height precision gauge blocks and FIG. 1I is a spatial domain fringe pattern image of the block structure of FIG. 1H. FIG. 1J is a frequency domain image obtained by performing a Fourier transformation upon the image of FIG. 1I. After circular band-pass filtering the area in the image of FIG. 1J for obtaining a spectrum image and then performing an inverse Fourier transformation upon the spectrum information, a Euler transformation and a phase unwrapping process is performed upon the Fourier-inversed image, the surface profile of the overlapping step-height gauge block can be reconstructed, as the reconstructed three-dimensional image shown in FIG. 1K and the cross-sectional image of FIG. 1L. In FIG. 1L, by the reconstruction resulting from the aforesaid conventional circular band-pass filter, the edges between each blocks in reconstructed image of the step-height block are rounded like arcs and not longer preserve the right angles in the original structure.
Therefore, it is in need of a method for acquiring phase information and relating system for measuring three-dimensional surface profile that are free from the aforesaid shortcomings.